Please refer to FIG. 1 to FIG. 4, which are schematic diagrams showing different exemplary sub-pixel arrangements in common flat-panel displays, such as liquid crystal displays (LCD), plasma display or organic light emitting diode (OLED) displays. Wherein, FIG. 1 shows a display screen 1 having R, G, and B sub-pixels in vertical strip configuration; FIG. 2 shows a display screen 1 having R, G, and B sub-pixels in mosaic configuration; FIG. 3 shows a display screen 1 having R, G, and B sub-pixels in delta configuration; and FIG. 4 shows a display screen 1 having R, G, and B sub-pixels in pentile configuration. As shown in FIG. 1 to FIG. 4, the display screen 1 is composed of N×M sub-pixels, in which N represents the total number of sub-pixels in a horizontal direction (X axis) of the display screen, and M represents the total number of sub-pixels in a vertical direction (Y axis) of the display screen. In addition, the horizontal position and the vertical position of any single sub-pixel in N×M display screen are represented respectively using the index i and j, whereas 0≦j≦N−1 and 0≦i≦M−1; and each single sub-pixel has a size of PH×PV, whereas PH represents the horizontal width of a single sub-pixel and PV represents the vertical height of a single sub-pixel. In the following description, a coordinate system of XYZ axes is used, and is defined according to the Right-hand rule with the three axes X, Y and Z to be at ring angle to each other in a manner that the X and Y axes define a horizontal direction and a vertical direction of a display while allowing the Z axis to be arranged perpendicular to the display screen. Moreover, it is common that the display screen is centered at the origin of the aforesaid coordinate system, and thus the aforesaid XYZ coordinate system can be referred as a screen coordinate system. Therefore, an image displayed on the aforesaid display screen can be represented as following:
                    V        =                              ∑                          i              =              0                                      M              -              1                                ⁢                                    ∑                              j                =                0                                            N                -                1                                      ⁢                          V              ⁡                              (                                  i                  ,                  j                                )                                                                        (        1        )                            wherein, V(i,j) represents the sub-pixel image data at position (i,j) of the display screen.Consequently, any multi-view image displayed on the screen can be represented as a composition of a plurality of single-view image Vk, whereas the single-view image can be defined as following:        
                              V          k                =                              ∑                          i              =              0                                      M              -              1                                ⁢                                    ∑                              j                =                0                                            N                -                1                                      ⁢                                          V                k                            ⁡                              (                                  i                  ,                  j                                )                                                                        (        2        )                            wherein, n is the total amount of view, k represents the index of view, and                    0≦k<n, n≧2; and            Vk (i,j) represents the sub-pixel image data of a single-view image Vk at position (i,j) of the display screen.                        
The following description relates to the shortcomings of a multi-view 3D image combination method that is disclosed in TW Pat. Publication No. 201320717. In the method disclosed in TW Pat. Publication No. 201320717, a multi-view combined 3D image is generated according to the following formula:
                              Σ          n                =                              ∑                          i              =              0                                      M              -              1                                ⁢                                    ∑                              j                =                0                                            N                -                1                                      ⁢                                          V                Λ                            ⁡                              (                                  i                  ,                  j                                )                                                                        (        3        )                            wherein, for the multi-view combined 3D images having a feature of slanting to the right, the index Λ is defined as:        
                    Λ        =                  Mod          [                                    int              [                                                j                  -                                      Π                    ×                                          int                      ⁡                                              (                                                                              i                            +                            Δ                                                    Q                                                )                                                                                            m                            ]                        ,            n                    ]                                    (        4        )                            for the multi-view combined 3D images having a feature of slanting to the left, the index Λ is defined as:        
                    Λ        =                  Mod          [                                    int              [                                                                    (                                          N                      -                      1                                        )                                    -                  j                  -                                      Π                    ×                                          int                      ⁡                                              (                                                                              i                            +                            Δ                                                    Q                                                )                                                                                            m                            ]                        ,            n                    ]                                    (        5        )            Similarly, VΛ (i,j) represents the sub-pixel image data of a single-view image VΛ at position (i,j) of the display screen; Λ represents a view number, and Λ<n, while n is the total amount of view; m is a number of sub-pixels of a smallest display unit in horizontal direction, while Q is a number of sub-pixels of a smallest display unit in vertical direction, and thereby, mQ represents the smallest display unit; Δ is a horizontal displacement phase; Π is a horizontal displacement amplitude, the index i and j are respectively a horizontal position number and vertical position number of each sub-pixel, whereas 0≦j≦N−1 and 0≦i≦M−1; and int is a round down integer function, and Mod is a function of taking a remainder.
The following description of shortcomings is provided using only formula (4) for illustration. Taking the 2-view combined 3D image Σn shown in FIG. 5 for example, for simplifying and displaying the 2-view combined 3D image Σn, whereas n=2, m=6, Q=2, Δ=0, and Π=1, it is defined by letting VΛ(i,j)=Λ, and thereby, when the number 0 is displayed at a position (i,j) of the display screen, it represents a left-view data and when the number 1 is displayed at a position (i,j) of the display screen, it represents a right-view data, or vice versa. That is, when the sub-pixel data at a position (i, j) of the display screen is replaced by the view numbers, i.e. VΛ(i, j)=Λ, the origin of the image at the position (i, j) relating to whether it is obtained from a left-view image or a right image is clearly indicated, and thus also the overall structural characteristic of the combined 3D image can be clearly demonstrated. In addition, when the value of Δ is changed, e.g. Δ=1, the amount of mQ sub-pixels in the smallest display unit can not be moved simultaneously to the right according to a horizontal displacement phase of Δ=1. As shown in FIG. 6, VΛ(0,0) and VΛ(0,6) are not 0, 1 in respective, but should be 1, 0, so that the amount mQ sub-pixels in the smallest display unit can be moved simultaneously to the left according to a horizontal displacement phase of Δ=1. Moreover, the multi-view 3D image combination disclosed in U.S. Pat. No. 6,064,424 can not be achieved using the formula (4) and (5), as shown in FIG. 7.
The following description relates to the shortcomings for designing a parallax barrier device that is disclosed in TW Pat. Publication No. 201320717, and is based upon a 2-view slantwise strip parallax barrier.
Please refer to FIG. 8, which is a schematic diagram showing a slantwise strip parallax barrier for 2-view images. In FIG. 8, a 2-view slantwise strip parallax barrier 30 is used and it is composed of a plurality of slantwise strip transparent elements 31 and a plurality of slantwise strip shield elements 32, whereas one barrier unit 33 in the 2-view slantwise strip parallax barrier 30 is defined to be the composition of one transparent element 31 and one shield element 32, and there are a plurality of such barrier units being arranged one next to another in a horizontal direction so as to form the 2-view slantwise strip parallax barrier 30. Notably, each transparent element 31 is formed in a width BH and with a slant angle θ, and also each shield element 32 is formed in a width BH and with a slant angle θ. Thus, the horizontal width of one barrier unit 33 will be PB=BHBH. It is noted that the parallax barrier 30 is used for displaying a 2-view 3D combined image Σn (n=2, m=3, Q=1, Π=1 and Δ=0) on a display screen 1, whereas VΛ(i, j)=0 indicates a left-view image L and VΛ(i, j)=1 indicates a right-view image R.
Please refer to FIG. 9, which is a schematic diagram showing a view separation principle for parallax barriers. In FIG. 9, the slantwise strip parallax barrier 30 is disposed in front of a display screen 1 at a distance LB away, and in a screen coordinate system of the display screen 1, for the 2-view combined 3D image Σn, the slantwise strip parallax barrier 30 may perform the optical effect of view separation on the combined 3D image Σn and provide multiple optimum viewing points (OVPs), such as OVP(L) and OVP(R), at an optimum viewing distance Z0, and perform the optical effect of view separation at each optimum viewing point to achieve the objective of respectively presenting a single-view image. Therefore, by locating the left eye 2 and right eye 3 of a viewer at the positions OVP(L) and OVP(R) in respective, the viewer is able to experience and see a 3D image.
In fact, it is feasible to define an optimum viewing plane at the optimum viewing distance Z0 that is arranged perpendicular to the Z axis of the screen coordinate system, as shown in FIG. 10, and the multiple optimum viewing points Pk.i.j(xc, yc, Z0) are located on the optimun viewing plane so that each of the optimum viewing points Pk.i.j(xc, yc, Z0) is enable to perform the optical effect of view separation for obtaining a corresponding single-view images. In FIG. 10, LH is the optimum horizontal interval between two neighboring optimum viewing points, and LV is the optimum vertical interval between two neighboring optimum viewing points, whereas, in general, LH is defined to be 63.5 mm which is the average interpupillary distance (IPD). Thus, on the horizontal direction, the aforesaid parameters in the slantwise strip parallax barrier can be defined by the following formulas:
                              B          H                =                                            D              H                        ⁢                          L              H                                                          D              H                        +                          L              H                                                          (        6        )                                                      B            _                    H                =                              (                          n              -              1                        )                    ⁢                      B            H                                              (        7        )                                          L          H                =                                            D              H                        ⁢                          B              H                                                          D              H                        -                          B              H                                                          (        8        )                                          tan          ⁢                                          ⁢          θ                =                                            P              H                                      QP              V                                =                                    D              H                                      mD              V                                                          (        9        )                                          Z          0                =                                            D              H                                                      D                H                            -                              B                H                                              ⁢                      L            B                                              (        10        )                                          D          H                =                  mP          H                                    (        11        )                                          D          V                =                  QP          V                                    (        12        )                            wherein, PH is a horizontal width of a sub-pixel;                    PV is a vertical height of a sub-pixel;            m is a number of sub-pixels of a smallest display unit in horizontal direction, while Q is a number of sub-pixels of a smallest display unit in vertical direction, and both in and Q are intergal that are larger than 1;            DH is the width of a smallest display unit in horizontal direction;            DV is the width of a smallest display unit in vertical direction.Consequently, as the horizontal width of the barrier unit 33 is defined by PB=BH+BH, the horizonatal width of the barrier unit 33 PB=nBH.In addition, the forgoing formulas (6) and (8) can be represented differently as following:                        
                              B          H                =                                                            Z                0                            -                              L                B                                                    Z              0                                ⁢                      D            H                                              (        13        )                                          L          H                =                                            Z              0                                      L              B                                ⁢                      B            H                                              (        14        )            On the other hand, on the vertical direction, the aforesaid parameters in the slantwise strip parallax barrier can be defined by the following formulas:
                              B          V                =                                                            Z                0                            -                              L                B                                                    Z              0                                ⁢                      mD            V                                              (        15        )                                          L          V                =                                            mD              V                        ⁢                          B              V                                                          mD              V                        -                          B              V                                                          (        16        )            Therefore, the relationship between BV, DH and θ can be obtained by substituting the formula (9) into the formula (15), as following:
                              B          V                =                                                            Z                0                            -                              L                B                                                    Z              0                                ⁢                                    D              H                                      tan              ⁢                                                          ⁢              θ                                                          (        17        )            The relationship between BH and BV can be obtained by dividing the formula (13) with the formula (17), as following:
                                          B            H                                B            V                          =                  tan          ⁢                                          ⁢          θ                                    (        18        )            The relationship between LH and LV can be obtained by dividing the formula (8) with the formula (16), as following:
                                          L            H                                L            V                          =                  tan          ⁢                                          ⁢          θ                                    (        19        )            Moreover, for those optimum viewing points Pk.i.j(xc, yc, Z0), the relationship between the parameters xc, yc, LH and LV are defined by the following formulas:xc=[n×i−(n−1)/2+j−k]×LH  (20)yc=k×LV  (21)Wherein, n is the total view number, i is the horizontal index of viewing zone, j is the view number, k is the vertical index of viewing zone, and, the plane where all Pk,i,j(xc, yc, Z0) existed is the plane Z=Z0 and is referred to as an “optimum viewing plane”. Therefore, as shown in FIG. 10, when i is set to be a fixed value, and j=0, the points of Pk,i,j construct a slanted line 20 of a slant angle θ, and on the other hand, when i is set to be a fixed value, and j=1, the points of Pk,i,j construct another slanted line 21 of a slant angle θ.
Please refer to FIG. 11, which is a schematic diagram showing an optimum left-viewing area. As shown in FIG. 11, the optimum viewing points Pk,i.0 is distributed on the slanted line 20, i.e. every point on the slanted line 20 can be an optimum viewing point for the left eye of a viewer. Moreover, since for each and every such optimum viewing point there can be a corresponding optimum viewing area being defined, and in this case, an optimum left-viewing area as the white-colored area shown in FIG. 11. The aforesaid description also applied to an optimum right-viewing area, as shown in FIG. 12.
In FIG. 11 and FIG. 12, each of the left-viewing area and the right-viewing area is formed as a slanted strip in a horizontal width LH, a vertical width LV and a slant angle θ. Thus, a viewer can simply locate his/her left eye and right eye inside the left-viewing area and the right-viewing area in respective, while maintaining both eyes roughly on a same level, (i.e. the display screen is set for landscape displaying) the viewer is able to experience and see a 3D image.
Since the view separation effect disclosed in TW Pat. Publication No. 201320717 is based upon a conventional display screen defined by Pv=3PH, therefore the formula (9) and formula (19) are changed into tan θ=⅓ and LV=3LH. Consequently, when right and left eyes are vertically arranged with respect to one another (i.e. the display screen is set for portrait displaying), the viewer is not able to see 3D images since LV is way larger than IPD.
Therefore, the method for designing a parallax barrier that is disclosed in TW Pat. Publication No. 201320717 is a specific theory. That is, the parallax barriers designed based upon the formulas (6)˜(19) is restricted by and corresponding to tan θ≦⅓. Moreover, since Q is defined to be an integer, the change of the slant angle θ is restricted. In addition, the design principle based upon the formulas (6)˜(19) can not cover all the slant-and-step parallax barrier designs, neither did it cover all the view separation devices that are composed of lenticular.